Question

Use function notation to write a recursive formula to represent the sequence: 3, 6, 12, … f(n) = f(n − 1) + 3 f(n) = f(n − 1) + 2 f(n) = f(n − 1) ⋅ 3 f(n) = f(n − 1) ⋅ 2

Answer 1

The answer is D) f(n) = f(n − 1) ⋅ 2

Answer 2

The recursive formula for the geometric sequence is given by:

$f(n) = 2f(n-1)$

In a geometric sequence, the quotient between consecutive terms is always the same, called common factor q. Thus, the recursive representation of a geometric sequence is:

$f(n) = qf(n-1)$

In this problem, the sequence is: 3, 6, 12, ...

Thus, the common factor is:

$q = \frac{12}{6} = \frac{6}{3} = 2$

Which means that the recursive formula is:

$f(n) = 2f(n-1)$

A similar problem is given at https://brainly.com/question/24138365